1. What is the Perimeter of Hendecagon?

The perimeter of a hendecagon (11-sided polygon) is the total length around its outer boundary. It represents the sum of the lengths of all eleven sides of the polygon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P \) — Perimeter of Hendecagon (m)
• \( d_4 \) — Diagonal across four sides of Hendecagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sin \) — Sine trigonometric function

3. Formula Explanation

Details: This formula calculates the perimeter of a regular hendecagon using the diagonal measurement that spans four sides. The trigonometric functions account for the angular relationships within the regular polygon structure.

4. Using the Calculator

Tips: Enter the diagonal measurement across four sides in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with eleven sides and eleven angles. When all sides and angles are equal, it's called a regular hendecagon.

Q2: Why use trigonometric functions in the formula?
A: Trigonometric functions help relate the diagonal measurement to the side length through the internal angles of the regular polygon (π/11 radians or approximately 16.36°).

Q3: What are typical applications of this calculation?
A: This calculation is useful in geometry, architectural design, engineering projects involving polygonal structures, and mathematical problem-solving.

Q4: Can this formula be used for irregular hendecagons?
A: No, this formula applies only to regular hendecagons where all sides and angles are equal. For irregular hendecagons, the perimeter is simply the sum of all side lengths.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hendecagons, though practical measurements may introduce some margin of error.